Abstract
Secure multi-party computation (MPC) protocols enable a set of n mutually distrusting participants P 1, ..., P n , each with their own private input x i , to compute a function Y = F(x 1, ..., x n ), such that at the end of the protocol, all participants learn the correct value of Y, while secrecy of the private inputs is maintained. Classical results in the unconditionally secure MPC indicate that in the presence of an active adversary, every function can be computed if and only if the number of corrupted participants, t a , is smaller than n/3. Relaxing the requirement of perfect secrecy and utilizing broadcast channels, one can improve this bound to t a < n/2.
All existing MPC protocols assume that uncorrupted participants are truly honest, i.e., they are not even curious in learning other participant secret inputs. Based on this assumption, some MPC protocols are designed in such a way that after elimination of all misbehaving participants, the remaining ones learn all information in the system. This is not consistent with maintaining privacy of the participant inputs. Furthermore, an improvement of the classical results given by Fitzi, Hirt, and Maurer indicates that in addition to t a actively corrupted participants, the adversary may simultaneously corrupt some participants passively. This is in contrast to the assumption that participants who are not corrupted by an active adversary are truly honest.
This paper examines the privacy of MPC protocols, and introduces the notion of an omnipresent adversary, which cannot be eliminated from the protocol. The omnipresent adversary can be either a passive, an active or a mixed one. We assume that up to a minority of participants who are not corrupted by an active adversary can be corrupted passively, with the restriction that at any time, the number of corrupted participants does not exceed a predetermined threshold. We will also show that the existence of a t-resilient protocol for a group of n participants, implies the existence of a t’-private protocol for a group of n′ participants. That is, the elimination of misbehaving participants from a t-resilient protocol leads to the decomposition of the protocol.
Our adversary model stipulates that a MPC protocol never operates with a set of truly honest participants (which is a more realistic scenario). Therefore, privacy of all participants who properly follow the protocol will be maintained. We present a novel disqualification protocol to avoid a loss of privacy of participants who properly follow the protocol.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-3-642-00468-1_29
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Almansa, J., Damgård, I., Nielsen, J.: Simplified Threshold RSA with Adaptive and Proactive Security. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 593–611. Springer, Heidelberg (2006)
Beaver, D.: Multiparty protocols tolerating half faulty processors. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 560–572. Springer, Heidelberg (1990)
Beaver, D.: Secure Multiparty Protocols and Zero-Knowledge Proof Systems Tolerating a Faulty Minority. Journal of Cryptology 4, 75–122 (1991)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness Theorem for Non-Cryptographic Fault-Tolerant Distributed Computation. In: Proceedings of the 20th ACM Annual Symposium on the Theory of Computing (STOC 1988), pp. 1–10 (1988)
Canetti, R.: Security and Composition of Multiparty Cryptographic Protocols. Journal of Cryptology 13, 143–202 (2000)
Catalano, D., Gennaro, R., Halevi, S.: Computing Inverses over a Shared Secret Modulus. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 190–206. Springer, Heidelberg (2000)
Chaum, D., Crépeau, C., Damgård, I.: Multiparty Unconditionally Secure Protocols. In: Proceedings of the 20th ACM Annual Symposium on the Theory of Computing (STOC 1988), pp. 11–19 (1988)
Dolev, D., Dwork, C., Waarta, O., Yung, M.: Perfectly Secure Message Transmission. Journal of the ACM 40, 17–47 (1993)
Feldman, P.: A Practical Scheme for Non-interactive Verifiable Secret Sharing. In: 28th IEEE Symposium on Foundations of Computer Science, pp. 427–437 (October 1987)
Fitzi, M., Hirt, M., Maurer, U.: Trading correctness for privacy in unconditional multi-party computation. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 121–136. Springer, Heidelberg (1998)
Gennaro, R., Rabin, M., Rabin, T.: Simplified VSS and Fast-track Multiparty Computations with Applications to Threshold Cryptography. In: 17th Annual ACM Symposium on Principles of Distributed Computing, pp. 101–111 (1998)
Goldreich, O., Micali, S., Wigderson, A.: How to Play any Mental Game. In: Proceedings of the 19th ACM Annual Symposium on the Theory of Computing (STOC 1987), May 25–27, pp. 218–229 (1987)
Herzberg, A., Jarecki, S., Krawczyk, H., Yung, M.: Proactive secret sharing or: How to cope with perpetual leakage. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 339–352. Springer, Heidelberg (1995)
Hirt, M., Maurer, U., Przydatek, B.: Efficient Secure Multi-party Computation. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 143–161. Springer, Heidelberg (2000)
Pedersen, T.: Non-Interactive and Information-Theoretic Secure Verifiable Secret Sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)
Rabin, T., Ben-Or, M.: Verifiable Secret Sharing and Multiparty Protocols with Honest Majority. In: Proceedings of the 21th ACM Annual Symposium on the Theory of Computing (STOC 1989), pp. 73–85 (1989)
Shamir, A.: How to Share a Secret. Communications of the ACM 22, 612–613 (1979)
Yao, A.: Protocols for Secure Computations. In: The 23rd IEEE Symposium on the Foundations of Computer Science, pp. 160–164 (1982)
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Ghodosi, H., Pieprzyk, J. (2009). Multi-Party Computation with Omnipresent Adversary. In: Jarecki, S., Tsudik, G. (eds) Public Key Cryptography – PKC 2009. PKC 2009. Lecture Notes in Computer Science, vol 5443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00468-1_11
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